Question

n Fig. 2, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then ∠QOR equals:

(A) 67°
(B) 134°
(C) 44°
(D) 46°

Answer 1

Given: ∠QPR = 46°
PQ and PR are tangents.
Therefore, the radius drawn to these tangents will be perpendicular to the tangents.
So, we have OQ ⊥ PQ and OR ⊥ RP.
⇒ ∠OQP = ∠ORP = 90^∘
So, in quadrilateral PQOR, we have
∠OQP +∠QPR + ∠PRO + ∠ROQ = 360^∘
⇒ 90° + 46° + 90° + ∠ROQ = 360^∘
⇒ ∠ROQ = 360^∘ − 226^∘ = 134^∘

Hence, the correct option is B.